
where \(\left|\mathcal {N}\right|\)  stands for half-normal distribution. It follows from Theorem 4.4.5 of [1]} that (with high probability) \(\Vert b(0)\Vert = \mathcal {O}\left(1\right)\) , \(\Vert W(0)\Vert = \mathcal {O}\left(\sqrt{m}\right)\) , and \(\Vert A(0)\Vert = \mathcal {O}\left(\sqrt{m}\right)\) . For \(C_1=C_2=C_3=1\) , we have \(\lambda _1= \mathcal {O}\left(\sqrt{m}\right)\) , \(\lambda _2= \mathcal {O}\left(\sqrt{m}\right)\) , \(\lambda _3= \mathcal {O}\left(1\right)\) .
We can choose \(\gamma >0\)  small enough to ensure \(\gamma _0 = 1/2\) . By using standard concentration argument and Lemma REF , we obtain
\(\Vert \hat{y}(0)\Vert  =\Vert Z(0)b(0)\Vert =\mathcal {O}\left(\left\Vert \Phi (0)\left[I_m-\gamma A(0)\right]^{-1}\right\Vert \right)=\mathcal {O}\left(\Vert X\Vert _F\right).\) 
